Refer to section 6.2 of the "SmartExtension API Specification" document that comes with the SmartExtension SDK:
Extensions implementing the Control API also have the possibility to control the state of the accessory display. The display can be controlled via the CONTROL_SET_SCREEN_STATE_INTENT.
As part of the Intent, you also need to specify what state you want to set. The following options are available:
* SCREEN_STATE_OFF
* SCREEN_STATE_DIM
* SCREEN_STATE_ON
* SCREEN_STATE_AUTO